U.S. patent application number 13/304783 was filed with the patent office on 2013-05-30 for system and method employing a hierarchical load feature database to identify electric load types of different electric loads.
The applicant listed for this patent is BIN LU, Mayura A. Madane, Santosh K. Sharma, Yi Yang, Prachi Zambare. Invention is credited to BIN LU, Mayura A. Madane, Santosh K. Sharma, Yi Yang, Prachi Zambare.
Application Number | 20130138669 13/304783 |
Document ID | / |
Family ID | 47045149 |
Filed Date | 2013-05-30 |
United States Patent
Application |
20130138669 |
Kind Code |
A1 |
LU; BIN ; et al. |
May 30, 2013 |
SYSTEM AND METHOD EMPLOYING A HIERARCHICAL LOAD FEATURE DATABASE TO
IDENTIFY ELECTRIC LOAD TYPES OF DIFFERENT ELECTRIC LOADS
Abstract
A method identifies electric load types of a plurality of
different electric loads. The method includes providing a
hierarchical load feature database having a plurality of layers;
including with each of a plurality of the layers a corresponding
load feature set, the corresponding load feature set of at least
one of the layers being different from the corresponding load
feature set of at least another one of the layers; including with
one of the layers a plurality of different electric load types;
sensing a voltage signal and a current signal for each of the
different electric loads; determining at least four different load
features from the sensed voltage signal and the sensed current
signal for a corresponding one of the different electric loads; and
identifying by a processor one of the different electric load types
by relating the different load features to the hierarchical load
feature database.
Inventors: |
LU; BIN; (Shanghai, CN)
; Yang; Yi; (Milwaukee, WI) ; Sharma; Santosh
K.; (Pune, IN) ; Zambare; Prachi; (Pune,
IN) ; Madane; Mayura A.; (Pune, IN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
LU; BIN
Yang; Yi
Sharma; Santosh K.
Zambare; Prachi
Madane; Mayura A. |
Shanghai
Milwaukee
Pune
Pune
Pune |
WI |
CN
US
IN
IN
IN |
|
|
Family ID: |
47045149 |
Appl. No.: |
13/304783 |
Filed: |
November 28, 2011 |
Current U.S.
Class: |
707/758 ;
707/E17.014; 707/E17.044 |
Current CPC
Class: |
G06N 3/088 20130101 |
Class at
Publication: |
707/758 ;
707/E17.044; 707/E17.014 |
International
Class: |
G06F 17/30 20060101
G06F017/30 |
Claims
1. A method of identifying electric load types of a plurality of
different electric loads, said method comprising: providing a
hierarchical load feature database comprising a plurality of
layers; including with each of a plurality of said layers a
corresponding load feature set, the corresponding load feature set
of at least one of said layers being different from the
corresponding load feature set of at least another one of said
layers; including with one of said layers a plurality of different
electric load types; sensing a voltage signal and a current signal
for each of said different electric loads; determining at least
four different load features from said sensed voltage signal and
said sensed current signal for a corresponding one of said
different electric loads; and identifying by a processor one of
said different electric load types by relating the different load
features to the hierarchical load feature database.
2. The method of claim 1 further comprising: employing a first one
of said layers having a plurality of load features selected from
the group consisting of true power factor, displacement power
factor, current total harmonic distortion, admittance, and a
voltage-current trajectory graphical representation.
3. The method of claim 2 further comprising: employing a second one
of said layers having a plurality of load features selected from
the group consisting of nominal power, distortion power factor,
current total harmonic distortion, a voltage-current trajectory
graphical representation, normalized third and fifth harmonics of
voltage and current, and high-frequency components of voltage and
current.
4. The method of claim 3 further comprising: employing a third one
of said layers having a plurality of load features selected from
the group consisting of transient on/off behavior, event detection,
and long-term operating mode patterns.
5. The method of claim 1 further comprising: selecting a plurality
of load features for each of said layers; and defining a plurality
of load categories or load sub-categories employing the load
features for some of said layers.
6. The method of claim 1 further comprising: employing said
providing the hierarchical load feature database as an offline
process; and employing said determining and said identifying by
said processor as a real-time process.
7. The method of claim 1 further comprising: employing said sensing
the voltage signal and the current signal for each of said
different electric loads in real-time; selecting a plurality of
load features for each of said layers; selecting a first load
feature set for a first one of said layers, and identifying one of
a plurality of different first load categories for a corresponding
one of said different electric loads for the first one of said
layers; selecting a second load feature set for a second one of
said layers, and identifying one of a plurality of different second
load sub-categories for the corresponding one of said different
electric loads for the second one of said layers; and selecting a
third load feature set for a third one of said layers, and
identifying one of said different electric load types for the
corresponding one of said different electric loads for the third
one of said layers.
8. The method of claim 1 further comprising: including with said
processor a power calculator to calculate power related quantities
for a plurality of said different electric loads.
9. The method of claim 1 further comprising: employing a first load
feature set of a first one of said layers; and employing a second
different load feature set of a second one and a third one of said
layers.
10. The method of claim 9 further comprising: employing a plurality
of load categories for the first one of said layers; employing a
plurality of load sub-categories for the second one of said layers;
and employing said plurality of different electric load types for
the third one of said layers.
11. The method of claim 9 further comprising: including with the
first load feature set a plurality of polynomial coefficients of a
voltage-current trajectory, and admittance; and including with the
second different load feature set thinness of a voltage-current
trajectory, and admittance.
12. The method of claim 1 further comprising: employing said
determining and said identifying by said processor as a machine
learning and pattern recognition process selected from the group
consisting of an artificial neural network process, a support
vector machine process, and a proximity analysis process.
13. The method of claim 1 further comprising: providing offline
training of said hierarchical load feature database by a
processor.
14. The method of claim 1 further comprising: providing said
identifying by said processor in real-time.
15. The method of claim 1 further comprising: identifying by said
processor a load operating mode of said one of said different
electric load types.
16. The method of claim 15 further comprising: selecting the load
operating mode from the list consisting of on, off, and
standby.
17. The method of claim 1 further comprising: employing the
hierarchical load feature database as a hierarchical and scalable
load feature database.
18. The method of claim 1 further comprising: including with said
corresponding load feature set a plurality of load features; and
including with each of the load features of said corresponding load
feature set a range of values for a corresponding one of a
plurality of load categories, a plurality of load sub-categories,
and said plurality of different electric load types.
19. A system comprising: a hierarchical load feature database
comprising a plurality of layers, one of said layers including a
plurality of different electric load types; a plurality of sensors
structured to sense a voltage signal and a current signal for each
of a plurality of different electric loads; and a processor
structured to: determine at least four different load features from
said sensed voltage signal and said sensed current signal for a
corresponding one of said different electric loads, and identify
one of said different electric load types by relating the different
load features to the hierarchical load feature database, wherein
each of a plurality of said layers includes a corresponding load
feature set, and wherein the corresponding load feature set of at
least one of said layers is different from the corresponding load
feature set of at least another one of said layers.
20. The system of claim 19 wherein the corresponding load feature
set includes a plurality of load features; and wherein each of the
load features of said corresponding load feature set includes a
range of values for a corresponding one of a plurality of load
categories, a plurality of load sub-categories, and said plurality
of different electric load types.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is related to commonly assigned, copending
U.S. patent application Ser. No. ______ filed ______, entitled
"System And Method Employing A Self-Organizing Map Load Feature
Database To Identify Electric Load Types Of Different Electric
Loads" (Attorney Docket No. 11-pEDP-702); and
[0002] U.S. patent application Ser. No. ______, filed ______,
entitled "System And Method Employing A Minimum Distance And A Load
Feature Database To Identify Electric Load Types Of Different
Electric Loads" (Attorney Docket No. 1'-pEDP-703).
BACKGROUND
[0003] 1. Field
[0004] The disclosed concept pertains generally to electric loads
and, more particularly, to methods of identifying electric load
types of electric loads. The disclosed concept also pertains to
systems for identifying electric load types of electric loads.
[0005] 2. Background Information
[0006] Electricity usage costs have become an increasing fraction
of the total cost of ownership for commercial buildings. At the
same time, miscellaneous electric loads (MELs) account for about
36% of electricity consumption of commercial buildings. Effective
management of MELs could potentially improve energy savings of
buildings up to about 10%. However, power consumption monitoring
and energy management of MELs inside commercial buildings is often
overlooked. In order to provide the MELs' energy consumption
conditions by load type to a building automation system (BAS), and,
consequently, to manage the MELs and reduce energy consumption
inside commercial buildings, there is a need to identify the
MELs.
[0007] Lam, H. Y. et al., "A novel method to construct taxonomy of
electrical appliances based on load signatures," IEEE Transactions
on Consumer Electronics, vol. 53, no. 2, 2007, p. 653-60, discloses
that a load signature is an electrical expression that a load
device or appliance distinctly possesses. Load signatures can be
applied to produce many useful services and products, such as,
determining the energy usage of individual appliances, monitoring
the health of critical equipment, monitoring power quality, and
developing facility management tools. Load signatures of typical
yet extensive loads are needed to be collected before applying them
to different services and products. As there are an enormous number
of electrical appliances, it is beneficial to classify the
appliances for building a well-organized load signature database. A
method to classify the loads employs a two-dimensional form of load
signatures, voltage-current (V-I) trajectory, for characterizing
typical household appliances. A hierarchical clustering method uses
a hierarchical decision tree or dendrogram to show how objects are
related to each other. Groups of the objects can be determined from
the dendrogram, to classify appliances and construct the taxonomy
of the appliances. The taxonomy based on V-I trajectory is compared
to the taxonomies based on traditional power metrics and
eigenvectors in prior studies.
[0008] In this taxonomy approach, only one set of load features is
utilized, and the hierarchical structure of appliances, a
dendrogram, is based on the selection of a distance value/threshold
between the groups in each level, or the height of a cluster tree.
In this approach, the selection of the distance/height will affect
how the hierarchical tree is built.
[0009] There is room for improvement in methods of identifying
electric load types of electric loads.
[0010] There is further room for improvement in systems for
identifying electric load types of electric loads.
SUMMARY
[0011] These needs and others are met by embodiments of the
disclosed concept, which employ a hierarchical load feature
database comprising a plurality of layers, including with each of a
plurality of the layers a corresponding load feature set, the
corresponding load feature set of at least one of the layers being
different from the corresponding load feature set of at least
another one of the layers, and including with one of the layers a
plurality of different electric load types.
[0012] In accordance with one aspect of the disclosed concept, a
method identifies electric load types of a plurality of different
electric loads. The method comprises: providing a hierarchical load
feature database comprising a plurality of layers; including with
each of a plurality of the layers a corresponding load feature set,
the corresponding load feature set of at least one of the layers
being different from the corresponding load feature set of at least
another one of the layers; including with one of the layers a
plurality of different electric load types; sensing a voltage
signal and a current signal for each of the different electric
loads; determining at least four different load features from the
sensed voltage signal and the sensed current signal for a
corresponding one of the different electric loads; and identifying
by a processor one of the different electric load types by relating
the different load features to the hierarchical load feature
database.
[0013] As another aspect of the disclosed concept, a system
comprises: a hierarchical load feature database comprising a
plurality of layers, one of the layers including a plurality of
different electric load types; a plurality of sensors structured to
sense a voltage signal and a current signal for each of a plurality
of different electric loads; and a processor structured to:
determine at least four different load features from the sensed
voltage signal and the sensed current signal for a corresponding
one of the different electric loads, and identify one of the
different electric load types by relating the different load
features to the hierarchical load feature database, wherein each of
a plurality of the layers includes a corresponding load feature
set, and wherein the corresponding load feature set of at least one
of the layers is different from the corresponding load feature set
of at least another one of the layers.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] A full understanding of the disclosed concept can be gained
from the following description of the preferred embodiments when
read in conjunction with the accompanying drawings in which:
[0015] FIG. 1 is a block diagram of a system to identify
miscellaneous electric loads (MELs) in accordance with embodiments
of the disclosed concept.
[0016] FIG. 2 is a representation of a hierarchical load feature
database of FIG. 1.
[0017] FIG. 3 is a plot of a voltage-current (V-I) trajectory of a
portable fan.
[0018] FIG. 4 is a plot of a V-I trajectory of a printer.
[0019] FIG. 5 is a plot of a V-I trajectory of an incandescent
lamp.
[0020] FIGS. 6A-6E are plots of measured voltage and current
waveforms versus time for a portable fan, a shredder, a DVD player,
a battery charger, and a set top box, respectively.
[0021] FIG. 7 is a block diagram of a self-organizing map (SOM)
based load classification/identification system in accordance with
embodiments of the disclosed concept.
[0022] FIG. 8A is representation of a basic SOM structure.
[0023] FIG. 8B is a representation of SOM showing how an input
relatively high-dimensional space is related to an example output
2-D map (or 2-D lattice of neurons).
[0024] FIG. 9 is a block diagram showing a hierarchical SOM
structure for MELs identification in accordance with an embodiment
of the disclosed concept.
[0025] FIG. 10 is a representation of an example nine-dimension
load feature vector including steady state and V-I trajectory
features and a two-dimensional representation of load features for
six example load types in accordance with an embodiment of the
disclosed concept.
[0026] FIG. 11 is a representation of a U-matrix.
[0027] FIG. 12 is a corresponding labeling map of all neurons for
the U-matrix of FIG. 11.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0028] As employed herein, the term "number" shall mean one or an
integer greater than one (i.e., a plurality).
[0029] As employed herein, the term "processor" shall mean a
programmable analog and/or digital device that can store, retrieve,
and process data; a computer; a workstation; a personal computer; a
microprocessor; a microcontroller; a microcomputer; a central
processing unit; a mainframe computer; a mini-computer; a server; a
networked processor; or any suitable processing device or
apparatus.
[0030] The disclosed concept is described in association with
example loads and example load features, although the disclosed
concept is applicable to a wide range of loads and a wide range of
load features.
[0031] The disclosed concept provides a method and system to
identify electric load types, load operating modes and/or load
health, by utilizing voltage and current signals of loads and
suitable data processing and/or pattern recognition processes. This
enables a wide range of MELs' identification technologies and MELs
energy management applications.
[0032] Referring to FIG. 1, an example MELs identification system 2
is shown. The system 2 includes a hierarchical load feature
database 4 comprising a plurality of layers (non-limiting examples
of which are shown in FIG. 2 as layers 6,8,10, it being appreciated
that more than three layers can be employed). One of the example
layers 10 of FIG. 2 includes a plurality of different example
electric load types 12. A plurality of sensors, such as the example
current sensor 14 and the example voltage sensor 16 for one load,
are structured to sense a current signal (i(t)) 18 and a voltage
signal (v(t)) 20 for each of a plurality of different electric
loads (four different example loads 22,24,26,28 are shown in
phantom line drawing, it being appreciated that any number of loads
can be employed).
[0033] The system 2 also includes a processor 30 structured to
determine at least four different load features 32 from the sensed
voltage signal 20 and the sensed current signal 18 for a
corresponding one of the different electric loads (e.g., example
load 26, as shown), and identify (at the example online
identification process 34) a load type 36 of the different electric
load types 12 by relating the different load features 32 to the
hierarchical load feature database 4.
[0034] As will be explained, each of a plurality of the layers
6,8,10 of FIG. 2 includes a corresponding load feature set, and the
corresponding load feature set of at least one of the layers 6,8,10
(e.g., without limitation, layer 6) is different from the
corresponding load feature set of at least another one of the
layers 6,8,10 (e.g., without limitation, layer 8 or layer 10).
[0035] The example system 2 includes the electrical sensors 14,16
coupled to a power circuit (e.g., to sense voltage, current and
power of plugged loads, such as example loads 22,24,26,28, at a
power outlet, intelligent receptacle, panelboard or load center, it
being appreciated that a wide range of different power circuits can
be employed). A load feature extractor 38 acquires load electrical
signatures in the form of a relatively high-dimensional feature
vector, which in this example is the at least four different load
features 32. The hierarchical load feature database 4, which is
preferably scalable, is obtained from an offline training process
40. The online identification process 34 identifies the electric
load type 36 by relating the high-dimensional feature vector to the
hierarchical load feature database 4.
[0036] Any suitable processor (e.g., without limitation, a
processor of a receptacle; a processor of a power strip; a
processor of a panelboard or load center; a processor of a building
or energy management system; a networked processor) runs the
example offline training process 40 for the hierarchical load
feature database 4.
[0037] Any suitable processor (e.g., without limitation, a
processor of a receptacle; a processor of a power strip; a
processor of a panelboard or load center; a processor of a building
or energy management system; a networked processor) runs the
example online load classification/identification process 34.
[0038] The processor 30 can include, an optional power calculator
42 used to calculate power related quantities (e.g., without
limitation, load current RMS values; real power consumption; power
factor). The power calculator 42 provides continuous power
monitoring for various loads of interest, and also facilitates load
feature extraction when load identification is needed.
[0039] Example features for the example first layer 6 of the
hierarchical load feature database 4 of FIG. 2 include: true power
factor (PF) (e.g., ratio of the real power flowing to a load to the
apparent power in the power circuit; a dimensionless number between
0 and 1 (or a percentage, e.g., 0.5 PF=50% PF)), displacement power
factor (e.g., in linear circuits having only sinusoidal currents
and voltages of one frequency, the power factor arises only from
the difference in phase between the current and voltage), current
total harmonic distortion (THD), normalized admittance, and V-I
trajectory graphical representations (e.g., without limitation,
area; number of segments; polynomial coefficients) as are discussed
in detail, below.
[0040] Example features for example second layer 8 of the
hierarchical load feature database 4 of FIG. 2 include: appliances
power (or nominal power), distortion power factor, current THD, V-I
trajectory graphical representations (e.g., without limitation,
polynomial coefficients, thinness ratio), normalized third and
fifth harmonics of voltage and current, and high-frequency
components of voltage and current signals.
[0041] The distortion power factor (I1,rms/Irms) describes how the
harmonic distortion of a load current decreases the average power
transferred to the load. THDi is the total harmonic distortion of
the load current. This assumes that the voltage stays undistorted
(i.e., sinusoidal, without harmonics). This simplification is often
a good approximation in practice. I1,rms is the fundamental
component of the current and Irms is the total current, both of
which are root mean square values.
[0042] The distortion power factor when multiplied by the
displacement power factor is the overall, true power factor or just
power factor (PF).
[0043] Example features for the example third layer 12 of the
hierarchical load feature database 4 of FIG. 2 include: transient
on/off behavior (e.g., without limitation, short-term harmonic
contents; transient energy content), event detection (e.g., load
turn on/off behaviors; load power fluctuation), and long-term
operating mode patterns (e.g., without limitation, operating
current/power profile of loads).
[0044] Another example load feature, K-factor, is linked with
harmonic content of current, and represents a heating effect due to
distorted current (e.g., for a supply transformer). K-factor is
defined by Equation 1.
K-factor=(I.sub.1.sup.2+(I.sub.2*2).sup.2+(I.sub.3*3).sup.2+ . . .
(I.sub.n*n).sup.2)/(I.sub.1.sup.2+I.sub.2.sup.2+I.sub.3.sup.2+ . .
. I.sub.n.sup.2) (Eq. 1)
wherein:
[0045] I.sub.1, I.sub.2 and I.sub.3 are first, second and third
order current harmonics, respectively; and
[0046] I.sub.n is the nth order current harmonic.
As the harmonic content of total I.sub.rms approaches zero,
K-factor approaches one.
[0047] An example load feature, Area, refers to the area enclosed
by a V-I trajectory. Area is proportional to the magnitude of the
phase shift between the voltage and the current. If current leads
voltage, then Area has a positive sign. If current lags voltage,
then Area becomes negative. Area is directly calculated from the
coordinates of the voltage and current points, (x.sub.i, y.sub.i),
on the V-I trajectory. The area, A, is given by Equation 2.
A = 1 2 i = 0 N - 1 ( x i , y i + 1 - x i + 1 y i ) ( Eq . 2 )
##EQU00001##
wherein:
[0048] N is the integer number of samples;
[0049] x.sub.i is a sample of voltage instantaneous value; and
[0050] y.sub.i is a sample of current instantaneous value.
[0051] FIG. 3 shows an example V-I trajectory 44 of a portable fan.
Here, the calculated Area value is 2.4.
[0052] Another example load feature eccentricity, E, is the measure
of the aspect ratio of a shape, and is the ratio of the length of
the major axis to the length of the minor axis. This feature helps
to identify the shape of the waveform. Eccentricity is calculated
from Equations 3-5.
[0053] Equation 3 provides the covariance matrix, C, of the
shape.
c = 1 N i = 0 N - 1 ( x i g x y i g y ) ( x i g x y i g y ) T = ( c
xx c xy c yx c yy ) ( Eq . 3 ) ##EQU00002##
wherein:
[0054] N is the integer number of samples;
[0055] x.sub.i is a sample of voltage instantaneous value;
[0056] y.sub.i is a sample of current instantaneous value;
[0057] T in Equation 3 is the matrix transpose operator;
[0058] (g.sub.x, g.sub.y) is the centroid of the V-I trajectory;
and
c xx = 1 N i = 0 N - 1 ( x i - g x ) 2 ##EQU00003## c xy = 1 N i =
0 N - 1 ( x i - g x ) ( y i - g y ) ##EQU00003.2## c yx = 1 N i = 0
N - 1 ( y i - g y ) ( x i - g x ) ##EQU00003.3## c yy = 1 N i = 0 N
- 1 ( y i - g y ) 2 ##EQU00003.4##
[0059] Equation 4 calculates the lengths of the two principle axes,
.lamda..sub.1 and .lamda..sub.2.
.lamda. 1 = 1 2 [ c xx + c yy + ( c xx + c yy ) 2 - 4 ( c xx c yy -
c xy 2 ) ] .lamda. 2 = 1 2 [ c xx + c xx - ( c xx + c yy ) 2 - 4 (
c xx c yy - c xy 2 ) ] ( Eq . 4 ) ##EQU00004##
[0060] Equation 5 calculates eccentricity, E.
E=.lamda..sub.2/.lamda..sub.1 (Eq. 5)
[0061] For example, for the portable fan V-I trajectory 44 of FIG.
3, the eccentricity value, E, is calculated to be 0.28.
[0062] Another example load feature thinness, T, is defined by
Equation 6.
T=4.pi.A/P.sup.2 (Eq. 6)
wherein:
[0063] A is area of a shape; and
[0064] P is perimeter of the shape.
[0065] Example features defined by polynomial coefficients are
established by polynomial curve fitting, which finds the
coefficients of a normalized voltage of degree n that fits the
normalized voltage to normalized current. Table 1 includes two
examples of V-I trajectories 46,48 (as shown in FIGS. 4 and 5) in
which their third order polynomial coefficients show distinct
results.
TABLE-US-00001 TABLE 1 V-I Third Order Polynomial Coefficients Type
of load Trajectory A B C D Printer Figure 4 0.5575 0.0921 -0.1846
-0.0473 Incandescent Figure 5 -0.0730 0.0202 1.0673 -0.0229
lamp
[0066] Tables 2-4 show examples of high-dimensional features that
are selected for the example first layer 6 load category, as well
as for the example layers 8,10 load sub-category/load type. The
load feature ranges for each load category and sub-category are
also given in Tables 2-4. Table 2 is an example of the selected
load category feature ranges for the first layer 6 and includes
minimum and maximum values of the four polynomial coefficients A-D
and admittance. Table 3 is an example of the selected load category
feature ranges for the X category of Table 2 for layers 8,10 and
includes thinness and admittance. Table 4 is an example of the
selected load category feature ranges for the NP category of Table
2 for layers 8,10 and includes minimum and maximum values of the
four polynomial coefficients A-D, admittance, and P/Q ratio (i.e.,
the ratio between real power and reactive power).
TABLE-US-00002 TABLE 2 Layer 1 Load Poly Coeff. A Poly Coeff. B
Poly Coeff. C Poly Coeff. D Admittance (Mho) Category Min Max Min
Max Min Max Min Max Min Max NP: -0.746 0.994 -0.079 0.164 -0.443
0.164 -0.085 0.016 0.000 0.023 X: -0.278 0.218 -0.031 0.130 0.094
1.088 -0.037 0.051 0.002 0.123 P: -0.770 0.984 -0.145 0.172 -0.430
1.656 -0.078 0.044 0.000 0.036 M: -0.230 0.784 -0.046 0.143 0.113
0.940 -0.077 0.027 0.001 0.124 R: -0.634 0.156 0.004 0.058 0.847
1.098 -0.036 0.021 0.002 0.126
TABLE-US-00003 TABLE 3 Thinness Admittance (Mho) X-Category Min Max
Min Max Fan -7.366E-05 1.169E-02 3.520E-05 1.581E-02 Shredder
6.393E-03 8.344E-03 2.729E-02 3.065E-02
TABLE-US-00004 TABLE 4 NP- Poly Coeff. A Poly Coeff. B Poly Coeff.
C Poly Coeff. D Admittance (Mho) P/Q Ratio Category Min Max Min Max
Min Max Min Max Min Max Min Max DVD -7.78E- 8.35E- -1.74E- 2.70E-
-3.91E- 1.64E+ -1.17E- 6.63E- 1.39E- 7.97E- 1.16E- 4.32E+ Player 01
01 02 01 01 00 01 03 04 03 01 00 Set Top 5.47E- 9.71E- -4.43E-
2.35E- -4.47E- -2.36E- -1.21E- -1.43E- 9.64E- 4.94E- 2.54E- 4.38E-
Box 01 01 03 02 01 01 02 03 04 03 01 01 Battery -3.23E- 5.64E-
-2.01E- 2.28E- -1.40E- 3.60E- -1.33E- 6.88E- 1.25E- 2.86E- 6.58E-
1.81E- Charger 01 01 01 01 01 01 01 02 04 04 02 01
TABLE-US-00005 TABLE 5 X-Category Thinness Admittance Coeff. A
Coeff. B Coeff. C Coeff. D Fan -7.34E-05 2.27E-03 8.07E-03 4.99E-03
9.08E-01 -3.90E-03 Shredder 8.94E-03 2.70E-02 -1.83E-01 2.30E-02
1.11E+00 1.09E-02
TABLE-US-00006 TABLE 6 NP-Category Coeff. A Coeff. B Coeff. C
Coeff. D Admittance P/Q Ratio DVD Player 3.38E-01 1.45E-02
-1.59E-01 -1.19E-02 1.39E-04 1.16E-01 Set Top Box 6.76E-01 1.01E-02
-3.14E-01 -8.76E-03 1.44E-03 2.74E-01 Battery Charger 5.64E-01
5.93E-02 -1.40E-01 -5.37E-02 1.32E-04 8.18E-02
[0067] FIGS. 6A-6E respectively show the measured voltage/current
waveforms 50,52,54,56 and 58 for a portable fan, a shredder, a DVD
player, a battery charger, and a set top box.
[0068] The calculated features for these five loads are presented
in Tables 5 and 6.
[0069] The examples, above, employ a common table for each of the
two example layers 8,10, although a relatively finer granularity
load classification/identification can be employed. For example,
although three example layers 6,8,10 are shown, the number of
layers can be four or greater. Also, the hierarchical layers may go
deeper depending on the level of granularity that can be achieved.
This can present the opportunity to achieve a scalable load ID.
[0070] For real-time load type identification, the online
identification process 34 acts (e.g., without limitation, as a
search engine) to identify the load that is being monitored by
relating a real-time extracted high-dimensional feature vector to
the hierarchical load feature database 4. The basic process
includes: (1) real-time measuring of current/voltage waveforms of a
load being monitored; (2) extracting the high-dimensional feature
vector of the load; (3) selecting the first layer feature set, and
identifying which load category the monitored load belongs to in
the first layer 6; (4) selecting the second layer feature set
(which may be different than the first layer feature set), and
identifying which load sub-category the monitored load belongs to
in the second layer 8; and (5) selecting the bottom layer feature
set (which may be different than the first and second layer feature
sets), and identifying the load type 36 as defined in the bottom
layer 12. Items (3) to (5) provide online identification of the
load type 36. These can also provide online identification of the
load operating mode 60 (e.g., without limitation, off, standby, on)
and load health.
[0071] The above results validate that the calculated load features
fall into the load feature ranges of the corresponding load
category and sub-category, as shown in Tables 2-4 and 5 and 6, and
the load type 36 is able to be identified through the load
category/type classification and identification from layer 6 to
layer 10.
[0072] The load category/type classification and identification can
be implemented by a wide range of machine learning and pattern
recognition processes, such as, for example and without limitation,
artificial neural network processes, support vector machine
processes, and proximity analysis processes.
[0073] In the disclosed concept, a different set of load features
is advantageously employed for each load category and each
sub-category classification/identification.
[0074] FIG. 2 and the above example features for each load category
layer represent non-limiting examples of defining load categories
and constructing a hierarchical load feature database 4 by
selecting suitable features for each category. However, there are
other example ways to define load categories, such as based on
electric code and regulation standards. For instance, the IEC
61000-3-2 Standard classifies appliances into four classes mainly
based on their power consumption and harmonics.
[0075] In FIG. 2, PFC represents Power Factor Correction, MFD
represents Multiple Functional Device, and TXM represents
Transformer.
[0076] Referring to FIG. 7, the disclosed concept provides a
Self-Organizing Map (SOM) based MELs classifier/identifier system
100 that extracts a relatively high-dimensional load feature vector
102 that is extracted to uniquely represent each reference load
type in a feature space. SOM is an ideal unsupervised training
method to construct an optimized load feature reference database by
providing a convenient 2-D or 3-D representation of a relatively
high-dimensional load feature database, such as database 4 of FIG.
2. This enables a simple and relatively fast online load
classification/identification for real-time implementation. To
reduce the crowdedness in the resultant SOM, a hierarchical SOM 104
is employed.
[0077] SOM is an ideal self-clustering tool, but is not designed as
a classifier. Hence, the disclosed concept preferably extends the
basic SOM to be supervised and employs a suitable decision-making
distance metric to construct an effective classifier based on
SOM.
[0078] The disclosed concept includes: (1) structuring a relatively
high-dimensional feature space 104 of MELs, in order that the
relatively high-dimensional feature vector of each load (extracted
from the measured current/voltage signals of each load) can be used
to uniquely distinguish itself from other loads; and (2) use of an
SOM based algorithm for load feature clustering in the SOM 104 and
load classification/identification 106 to enable an optimized load
feature reference database, and a relatively fast and simple
real-time implementation.
[0079] The SOM based load classification/identification system 100
includes V/I waveform measurement 108. The system 100 also
includes: (1) relatively high-dimensional load feature extraction
110; (2) an input relatively high-dimensional space is related to
an output, for example and without limitation, 2-D map (or 2-D
lattice of neurons 112) (FIG. 8B); (3) the hierarchical SOM 104
having a top-layer SOM 114, with load feature clustering by load
categories, and second-layer SOMs 116, with load feature clustering
by load type under each load category; and (4) the SOM classifier
construction 106, which preferably employs a suitable distance
metric 118 to provide (5) load identification results 120.
[0080] Still referring to FIG. 7, relatively high-dimensional load
feature extraction 110 proceeds as follows. Different
features/signatures of MELs are investigated and extracted from the
actual operational currents and voltages of loads, including the
following aspects of load characteristics: (1) steady state current
waveform and power quality related quantities; (2) voltage-current
(V-I) trajectory graphical representation under start-up and
steady-state conditions; (3) transient state characteristics of
load current, including short-term harmonic contents, and transient
power contents; and (4) load event detection, operating status
profile, and operating modes patterns. The main objective of the
load feature extraction 110 is to select a relatively
high-dimensional load feature space, in order that every cluster of
load feature vectors can uniquely represent one type of load in the
reference load database 4 (FIG. 2).
[0081] In the second part of the system, SOM uses a relatively
low-dimensional grid, such as 112 (FIG. 8B), of neurons 124 (FIGS.
8A and 8B) to capture and represent relatively high-dimensional
input data (e.g., a relatively high-dimensional load feature space
for identification of electric loads). This mapping preserves
topological properties in vector space. During a training process,
all neurons compete for the right to respond to the input data,
although only one neuron will win at a time. The training result of
a basic SOM is a low-dimensional (e.g., without limitation,
typically, two-dimensional), discrete grid of neurons with similar
characteristics as for training samples from the training
process.
[0082] FIG. 8A shows an example 4-by-4 neuron map 122. Each neuron
124 is fully connected to the input layer 126. Each neuron 124
could either possess unique characteristics or belong to a subgroup
of other neurons 124.
[0083] Each neuron 124 in the SOM grid 112 (FIG. 8B) is assigned
with: (1) a topological position (i.e., an x-y coordinate in the
example two-dimensional output grid), which is fixed during
training; (2) a parametric reference (also called model or
codebook) vector of weights of the same dimension as the input
training data, which is time-varying during training; and (3) a
fixed neighborhood function which defines a neighborhood (e.g.,
without limitation, a circle or a square in the example
two-dimensional output grid) centered at a neuron with a relatively
large initial radius, but decreasing with time, which is a unique
feature of the SOMs 114 or 116 (FIG. 7). At each time step, if a
neuron is the winner, then all neurons within its radius will
update their weights. This method of training is called a
"winner-takes-all" strategy.
[0084] An SOM, such as 114 or 116 (FIG. 7), can have K neurons in
the output grid 112 (FIG. 8B), where K is a suitable positive
integer. For neuron i, if the training data consists of vectors x
of l-dimensions, x=[x.sub.1, x.sub.2, x.sub.3, . . . , x.sub.l],
then each neuron is assigned a corresponding weight vector m also
of l-dimensions:
m.sub.i=[m.sub.i1,m.sub.i2,m.sub.i3,m.sub.il].
Before the training process starts, the m.sub.i values are
initialized. A suitable choice of the initial values can make the
training process converge in a stable and relatively fast
manner.
[0085] There are two versions of the basic SOM training algorithm:
the original incremental training, and the batch training. The
following describes the basic incremental SOM training algorithm,
which has seven steps.
[0086] First, all neurons' weight vectors m.sub.i, are initialized,
where i=1, 2, . . . , K.
[0087] Second, an input vector of data x=[x.sub.1, x.sub.2,
x.sub.3, . . . , x.sub.l] is chosen randomly from the training data
and is presented to all of the neurons via variable scalar weights
.mu..sub.ij, which are generally different for different
neurons.
[0088] Third, every neuron is examined to calculate which one
possesses a weight vector that is closest to the input vector in
the sense of minimum distance. In some embodiments, the Euclidean
distance function d is used to measure closeness, with k being an
index of the various dimensions l, such that:
d ( m i , x ) = k = 1 l ( m ik - x k ) 2 . ##EQU00005##
[0089] Fourth, the so-called "winning neuron" is the one for which
d is a minimum. Signified by the subscript c, the winning neuron is
the "Best Matching Unit" (BMU):
c=arg min{.parallel.x-m.sub.i.parallel.}.
[0090] Then, the radius of the neighborhood N.sub.c(t) of the BMU c
is calculated according to the neighborhood function h.sub.ci(t),
where i denotes any other neuron than the BMU. This neighborhood
function is selected such at h.sub.c,i(t).fwdarw.0 when
t.fwdarw..infin.. Usually h.sub.c,i(t) is chosen as a function of
the distance between r.sub.c and r.sub.i, where between r.sub.c and
r.sub.i are the location vectors of neurons c and i, respectively.
For example, the neighborhood function can be written in the
Gaussian form:
h c , i ( t ) = .alpha. ( t ) exp ( - r c - r i 2 2 .sigma. ( t ) )
, ##EQU00006##
wherein:
[0091] .alpha.(t) is another scalar-valued "learning rate factor"
that is monotonically decreasing with time; and
[0092] .sigma.(t) defines the width of the kernel which corresponds
to the radius of the neighborhood N.sub.c(t); this is usually set
to a relatively high value early in the training process to produce
a rough training phase.
[0093] Sixth, any neuron that has a Euclidean distance to the BMU
less than the neighborhood radius is considered to be inside of the
BMU's neighborhood and its weight vector is adjusted to make it
resemble the input vector more closely. The closer a neuron is to
the BMU, the more the neuron's weight vector gets altered during
the training process:
m.sub.i(t+1)=m.sub.i(t)+h.sub.c,i(t)[x(t)-m.sub.i(t)],
wherein:
[0094] t=0, 1, 2, . . . is an integer denoting the discrete time
index.
[0095] Seventh and finally, the second step, above, is repeated for
N iterations, where N is the total number of input training vectors
of data x presented to the SOM 104 (FIG. 7). N may exceed the
number of data vectors in the database 4 of FIG. 2, in which case
the training vector is each time selected randomly from the data
vector base. Past experience shows that for good performance N
should be at least about 500 times the number of neurons 124 (FIGS.
8A and 8B).
[0096] One of the main advantages of SOM is that SOM is able to
cluster load features by nature. In other words, by applying a
neighborhood function scheme, SOM is not only able to distinguish
the difference between clusters of load features, but also to
organize the similarity among the features by preserving the
topological properties of the input space. This means that data
points that are relatively close or share relatively many common
features in the input space are mapped to neurons that are
positioned close to one another to form a so-called cluster.
Examples of load clusters 128,130,132,134,136,138 are shown in FIG.
10. The SOM 104, therefore, converts complex, nonlinear statistical
relationships between relatively high-dimensional data items into
relatively simple geometric relationships on, for example and
without limitation, a two-dimensional grid. As it thereby
compresses information, while preserving the most important
topological and metric relationships, the SOM 104 can also be
considered to produce some degree of abstractions. This advantage
is especially beneficial to MELs identification, because the
resultant map provides a natural tolerance to the possible
diversities of same load type, but from different MEL manufacturers
with different power ratings.
[0097] Referring to FIG. 9, after the relatively high-dimensional
load feature space is selected, SOM is used to map the relatively
high-dimensional load feature data or vector 102 to a relatively
low-dimensional (e.g., without limitation, 2-D or 3-D) space by
implementing a competitive and unsupervised training process to
cluster and organize all the load features in a resultant, say 2-D,
map. How the input relatively high-dimensional space 140 is related
to the output 2-D map (or 2-D lattice of neurons) 142 is shown in
FIG. 10.
[0098] As the number of reference load types increases, the result
map gets crowded. As a result, a hierarchical SOM 104 of FIG. 7 is
employed. FIG. 9 shows one example of a suitable SOM structure,
where the first layer SOM 114 can include the following example
load categories: (1) resistive appliances 144; (2) motor driven
appliances 146; (3) electronically fed appliances 148; (4)
non-linear loads 150 with direct AC connections; and (5) unknown
152 (others). The second layer 116 includes four example sub-SOMs
154,156,158,160, each of which represents the load type reference
database of one load category 144,146,148,150. Each sub-SOM
154,156,158,160 contains the load feature reference database for
all load types that belong to one load category.
[0099] There are several advantages of this proposed structure. The
structure helps to reduce the crowdedness of the resultant SOMs. It
enables the load identification to be expanded and scaled-up as the
number of load types increases. Last, but not least, it facilitates
the subtle feature extract/selection for loads especially with the
most similarities.
[0100] FIG. 7 shows the SOM classifier 106. SOM is an ideal
self-clustering tool, but is not believed to be an effective
classifier. A known distance metric, called a unified distance
matrix (U-matrix), can be used to setup the boundaries among all
the clusters 128,130,132,134,136,138 in the map 142. There are
several disadvantages associated with this metric. As the value of
each entry of U-matrix is defined to be the average
distance/difference from itself to adjacent entries, the boundaries
tend to be ambiguous (e.g., not crisp). At the same time, this does
not provide an identification confidence level criteria, which is
discussed below in connection with Equation 10.
[0101] Another advantage of SOM is that the boundaries among the
clusters 128,130,132,134,136,138 in the map 142 define the
un-identified (unknown) loads automatically. The U-matrix is a
known conventional way to represent information about an SOM. The
U-matrix illustrates the weight vectors in the SOM by showing the
distances between adjacent pairs of neurons. For each neuron, the
distance between itself and its adjacent neurons (the number of
which depends on its neighborhood topology) is calculated and
presented with different colorings (not shown) or a gray scale
image (not shown). An example U-matrix 162 is shown in FIG. 11, and
its corresponding labeling map 164 of all neurons 165 is shown in
FIG. 12, in which the boundaries are manually marked out by curves
166,168,170,172. In FIG. 11, the example U-matrix 162 visualizes
distances between neighboring neurons, and helps to see the cluster
structure. The relatively darker regions (representing relatively
high values) (not shown) indicate a cluster boundary. FIG. 12 shows
the example labeling map 164 with labels.
[0102] As a non-limiting example, various load feature vectors of
nine example loads are presented to an example 50-by-50 SOM for
clustering. The loads are labeled as follows: (1) 2 set top boxes
(STB) and 1 DVD player (labeled by "1" in FIG. 12); (2) 1 space
heater (labeled by "2" in FIG. 12); (3) 1 plasma TV (labeled by "3"
in FIG. 12); and (4) 1 LCD TV, 1 LED TV, 1 LCD monitor, and 1
desktop computer (labeled by "4" in FIG. 12).
[0103] FIGS. 11 and 12 show that the boundaries of clusters from
the U-matrix 162 and the boundaries 166,168,170,172 from the
labeling map 164 are matched. Relatively lighter regions (not
shown) depict the relatively closely spaced neurons and relatively
darker regions (not shown) indicate the relatively more distant
neurons. Thus, groups of relatively light regions (not shown) can
be roughly considered as being a cluster. The relatively dark
regions (not shown), on the other hand, represent the boundary
regions that are not identified with a cluster and correspond to
gaps in the data.
[0104] The testing input data can be easily classified by looking
at the best-match neuron (e.g., via an example Euclidean distance,
or an example Mahalanobis distance metric as is discussed below in
connection with Equation 7) from the resultant SOM of this data. If
the point's best-match lies inside a cluster-region (i.e., a
relatively light region) (not shown) on the U-Matrix 162, then the
input data is classified to that cluster. If the best-match lies in
a relatively dark region (not shown) in the U-matrix 162, then no
classification of this point can be assigned. This is in particular
the case if the dataset possesses new features (i.e., aspects that
were not included in the data learned so far). With this approach,
for example, outliers, erroneous or unknown data are easily
detected.
[0105] The disclosed concept provides a decision-making technique
of a distance metric of the average distance among the neurons. The
disclosed concept preferably provides a suitable improved decision
metric by taking advantage of statistical information of the data
space. The basic SOM is trained by unsupervised learning as was
discussed above. That is, the training data vectors are not labeled
and no class identity information is attached or employed during
the learning process. Such unsupervised SOMs are not intended for
pattern recognition, but rather clustering, visualization and
abstraction. In order to apply the SOM 104 to a statistical pattern
recognition problem, the unsupervised SOM needs to be modified to
be a so-called supervised SOM.
[0106] To make the SOM 104 (FIG. 7) supervised, it is assumed that
there are M known classes of load types, .omega..sub.1,
.omega..sub.2, . . . , .omega..sub.M, and that each input load
feature vector is pre-assigned to one of the classes. Each input
load feature vector x remains unchanged in its values, but is
labeled by a string containing its pre-given class identity. The
input load feature vector x is augmented to be x.sub.a=[x.sup.T,
x.sub.q.sup.T].sup.T where x.sub.q is the numerical class identity
vector, and T is the matrix transpose operator. For instance,
x.sub.q can be a unit vector with its components assigned to one of
the known M classes. The augmented x.sub.a is used in training but
only x is considered in classification. In other words, the load
feature vector for training is extended to a greater dimension.
When the training is finished, neurons that have become the BMU to
one or more input vectors are classified into one of the classes by
a voting mechanism. The voting mechanism means that if a neuron
becomes the BMU to multiple input classes (each for probably
multiple times), then it is classified into the class for which it
has been the BMU for the greatest number of times. Neurons that
have never been a BMU to any input vector are marked as
"unclassified".
[0107] Formally, the supervised SOM includes: (1) M known classes
of interested subjects, .omega..sub.1, .omega..sub.2, . . . ,
.omega..sub.M, with class identity labels z.sub.1, z.sub.2, . . . ,
z.sub.M, respectively; (2) K neurons, n.sub.1, n.sub.2, . . . ,
n.sub.K, with weight vectors m.sub.1, m.sub.2, . . . , m.sub.K,
respectively; and (3) each weight vector m.sub.i is of l
dimensions: m.sub.i=[m.sub.i1, m.sub.i2, m.sub.i3, . . . ,
m.sub.il].
[0108] After training, a subset of K.sub.s<K neurons is
classified by the voting mechanism, that is, each of them is
classified into one of the pre-defined known classes. When an
unknown load feature vector x is presented to the SOM 104 (FIG. 7),
x is compared to all K.sub.s classified neurons and is classified
to be within that same class as the neuron that has the minimum
distance to x in the vector space.
[0109] Although the original SOM can be extended to supervised
learning and classification, its nature leads to many limitations
for the purpose of electric load identification. To fully utilize
the information contained in the training data and to achieve
relatively better classification performance, statistical distance
measurement between point and point, between point and class, and
between class and class can be adopted to replace the deterministic
Euclidean distance function, as was discussed above. A modified
training method can also improve the performance.
[0110] The training process of the supervised SOM (SSOM) is the
same in nature as the training process of the unsupervised SOM;
that is, to cluster the input feature patterns by their nature and
then to classify them. However, because of possible diversities of
same load type, but from different manufacturers with different
power ratings, the input data from different classes may overlap
with each other. In another words, a certain data vector in one
class could have similar values as another data vector in another
class, which could introduce an identification error. To fully
utilize all the information (e.g., without limitation, average
feature values and their variances) contained in the training data,
the first step is to extract the statistical information. That is,
as all the load feature vectors are labeled, the mean vector and
the covariance matrix of the load feature vectors of each class can
be computed.
[0111] For class .omega..sub.i, let y.sub.i and .SIGMA..sub.i
denote the mean and covariance, respectively, of all vectors within
this class. Then, the diversity information is contained in the M
mean vectors and the M covariance matrices, which can be used in
the initialization of the SOM 104. In the third step of the basic
incremental SOM training algorithm, above, the Euclidean distance
function is replaced with the known Mahalonobis distance function,
which is a statistical distance measure. See Mahalanobis, P. C.,
"On the generalised distance in statistics," Proceedings of the
National Institute of Sciences of India, vol. 2, 1936, pp. 49-55.
This is a useful way of determining similarity of an unknown sample
set to a known set. The Mahalonobis distance d.sub.M between two
vectors x and y is given by Equation 7:
d.sub.M(x,y).sup.2=(x-y).sup.T.SIGMA..sup.-1(x-y) (Eq. 7)
Equation 7 defines the Mahalanobis distance d.sub.M of the
multivariate input load feature vector x from a neuron's weight
vector y. The Mahalanobis distance (or "generalized squared
interpoint distance" for its squared value in Equation 7) can also
be defined as a dissimilarity measure between two random vectors
x,y of the same distribution with the covariance matrix .SIGMA..
.SIGMA. can uniformly take the average of the within-class
covariance matrix for each class or the total covariance matrix of
all training data. Considering the nature of the data available in
the electric load identification problem, a more precise option is
that if x is an input feature vector and y belongs to class
.omega..sub.i, then take .SIGMA.=.SIGMA..sub.i. In this way, the
statistical information can be fully utilized.
[0112] After completing the training, the final step is to replace
the Euclidean distance d.sub.E function with the following
point-to-cluster function in the SSOM, where Tr( ) denotes the
trace of a square matrix (which is the sum of the elements on the
main diagonal from the upper left to the lower right of the square
matrix).
d.sub.E(x,.omega..sub.i).sup.2=(x-y.sub.i).sup.T(x-y.sub.i)+Tr(.SIGMA..s-
ub.i) (Eq. 8)
This is, in fact, the average squared Euclidean distance from the
measured input load feature vector x to every point in class
.omega..sub.i. Then, the identification utilizes the statistical
information contained in the training data.
[0113] SOM is an ideal self-clustering tool, but is not designed as
an effective classifier. The identification decision made is hard
(i.e., an absolute decision), and does not provide an
identification confidence level criteria. This is not a desired
result, since errors often exist and no classifier can give a
desired 100% success rate. Instead, a soft decision may be desired,
which will indicate the probability of a particular load belonging
to a particular class. A hard decision can then be made based on
the soft probabilities, if needed. This problem comes from the fact
that although SOM employs a probability-related mapping, it does
not model and use the input data distribution density. To solve
this problem, a hybrid supervised SOM (SSOM)/Bayesian decision
making framework is disclosed as follows.
[0114] The Bayesian decision theory is a statistical approach,
which takes variation of the patterns as well as costs and risks
into consideration and classifies an unknown pattern in the most
probable sense. Given a classification task of M classes,
.omega..sub.1, .omega..sub.2, .omega..sub.M, and an unknown pattern
which is represented by a feature vector x, the Bayes classifier
classifies x as .omega..sub.j, which maximizes the conditional a
posteriori probabilities:
.omega. j = arg max i Pr ( .omega. i | x ) , i = 1 , 2 , , M ,
##EQU00007##
which is usually called a maximum a posteriori (MAP) classifier.
See Theodoridis, S. et al., "Pattern Recognition", Fourth Ed.,
Academic Press, 2008, ISBN: 978-1597492720. That is, each a
posteriori probability represents the probability that the unknown
pattern belongs to each respective class .omega..sub.i, given that
the observed feature vector is x. The Bayes rule is shown in
Equation 9:
Pr ( .omega. i | x ) = p ( x | .omega. i ) Pr ( .omega. i ) p ( x )
( Eq . 9 ) ##EQU00008##
wherein:
[0115] Pr(.omega..sub.i) denotes the a priori probability of the
respective class .omega..sub.i, and
[0116] p(x) is the probability density function (pdf) of x.
In a MAP classifier, p(x) is not needed and is not taken into
account during the classification. The a priori probabilities
Pr(.omega..sub.i), i=1, 2, . . . , M, can be estimated from the
available training feature data. Therefore, p(x|.omega..sub.i), the
likelihood function of x with respect to .omega..sub.i, is the only
difficulty in the MAP classifier. Note that when the load feature
vectors take only discrete values, the density function
p(x|.omega..sub.i) becomes probabilities and is usually denoted by
Pr(x|.omega..sub.i). In other words, an accurate estimation of the
underlying environmental pdf needs to be derived from the available
data.
[0117] It is well known that if the individual load features
x.sub.j, j=1, 2, . . . , l, are assumed to be statistically
independent, then it is true to have:
p ( x | .omega. i ) = k = 1 l p ( x k | .omega. i )
##EQU00009##
See Theodoridis, S. et al., above. A more descriptive term for the
underlying probability model would be "independent feature model".
Furthermore, an unknown feature vector x=[x.sub.1, x.sub.2,
x.sub.3, . . . , x.sub.l] is classified to be the class:
.omega. m = arg max .omega. i k = 1 l p ( x k | .omega. i ) , i = 1
, 2 , , M ##EQU00010##
[0118] The above model is also called the Naive Bayes classifier.
This assumes that the presence (or absence) of a particular feature
of a class is unrelated to the presence (or absence) of any other
feature of the same class. For an electric load identification
problem, depending on the load feature set selected, the
independence assumption could be reasonable.
[0119] The Naive Bayes classifier can be directly applied to the
identification of electric loads without incorporating an SOM. In
the disclosed concept, the Bayes decision theory is preferably
combined with the disclosed SSOM. The advantage of utilizing the
statistical information from the SOM neuron grid instead of
directly using the training data is that the estimation of the pdf
of x with respect to .omega..sub.i, p(x|.omega..sub.i), can be
greatly simplified while preserving accuracy and efficiency.
[0120] As was discussed above, one neuron is selected to be the BMU
at each training step and is labeled to be the same class as the
input load feature vector. When the training is complete, each
neuron could have been the BMU to load feature vectors from several
different pre-known classes and, thus, labeled differently or have
never been a winner. This observation contains rich and important
information, which has generally been ignored as the voting
mechanism is applied when the training is completed to determine
each neuron's final class label. For later reference, the history
of each neuron, which records how many times it has been a BMU to
input data vectors and to which class each data vector belongs, is
called "the BMU history" information.
[0121] Although many known methods are available to estimate the
pdf p(x|.omega..sub.i), they require a significant amount of
computing resources and time. Furthermore, it is, in fact, not
necessary to estimate a continuous pdf, but rather to estimate the
values of the pdf at given conditions, and the latter is much
faster and easier. The problem has, therefore, now degenerated to
estimation of the probability of certain discrete values. This
degeneration method is expected to work because of the fact that
there is a relatively large amount of samples of x to make a
sufficiently accurate estimation of the continuous density.
[0122] For example and without limitation, for a load feature set
(i.e., of average values per cycle) where there are 3600 data
points for each load and there are 10,800 data points available for
training even if only three loads are involved. Considering the
fact that x(t) is in the range of [0,1] at all times as well as the
example, non-limiting predetermined resolution of the samples is
only about 10.sup.-4, x(t) can be assumed to be quantized to x[k]
at the level of about 10.sup.-4, where k is an index. Thus, there
are 10.sup.4 values of x and part of them are observed in the
samples (multiple times). Based on the number of observed times,
the probability of each quantized value x with respect to each
class can be calculated using the BMU history information. The
probability of other unobserved values can be estimated using
suitable methods, such as interpolation. Formally, for each
quantized x[k], assume that it appears a total of T.sub.k times,
including T.sub.k1 times for the BMU to class .omega..sub.1,
T.sub.k2 times for the BMU to class .omega..sub.2, . . . , and
T.sub.kM times for the BMU to class .omega..sub.M, then:
Pr ( .omega. i | x [ k ] ) .apprxeq. T ki T k ( Eq . 10 )
##EQU00011##
For quantized values x[k] that have no BMU history, the value
Pr(.omega..sub.i|x[k']) can be estimated using linear interpolation
or other suitable nonlinear methods.
[0123] A test can be conducted to validate the above disclosed SSOM
algorithm with an extended classification and decision-making
mechanism. Three types of testing scenarios are considered: (1) a
data file of a known load model that is also used in training,
expecting 100% confidence and a 100% testing correct rate; (2) a
data file of a known load model that is not used in training, but
other data files of this model are used in training, expecting a
relatively lower correct rate than the first testing scenario; and
(3) a data file of a known load model, but never used in training,
expecting a relatively lower correct rate than the second
scenario.
[0124] The following types of loads were tested under the three
scenarios above, and the preliminary results are summarized in
Table 7. Eight non-limiting example steady state features used for
this test include: (f1) displacement power factor; (f2) current
total harmonic distortion (THD); (f3) current RMS value; (f4)
current crest factor; (f5) current 3.sup.rd order harmonic
amplitude; (f6) current 3.sup.rd order harmonic phase angle (with
respect to voltage); (f7) current 5.sup.th order harmonic
amplitude; and (f8) current 5.sup.th order harmonic phase angle
(with respect to voltage).
TABLE-US-00007 TABLE 7 Successful Likelihood Load Types Scenario
Rate Probability Brand A LCD TV #1 100% 100% Brand B Set Top Box #1
100% 100% Brand C Microwave Oven #1 100% 100% Brand D Space Heater
#1 100% 100% Brand E Laptop Computer #2 91% 98.8% Brand F LCD TV #3
99% 100% Brand G Microwave Oven #3 97.3% 98%
[0125] FIG. 10 shows an example set of results by applying SOM for
load classification and identification. The non-limiting example
test loads include: (1) compact fluorescent lamp (CFL); (2)
fluorescent lamp (FL); (3) incandescent lamp; (4) DVD player; (5)
LCD television (TV); and (6) fan. The extracted relatively
high-dimensional (e.g., without limitation, 9 dimensions) feature
vector 140 is also shown.
[0126] Six non-limiting example steady state features 174 include:
(f1) displacement power factor; (f2) true power factor; (f3)
current total harmonic distortion (THD); (f4) current K-factor;
(f5) current crest factor; and (f6) admittance (or the inverse of
impedance (Z)).
[0127] The example current crest factor or peak-to-average ratio
(PAR) or peak-to-average power ratio (PAPR) is a measurement of a
waveform, calculated from the peak amplitude of the waveform
divided by the RMS value of the waveform. It is therefore a
dimensionless quantity. While this quotient is most simply
expressed by a positive rational number, in commercial products it
is also commonly stated as the ratio of two whole numbers, e.g.,
2:1. In signal processing applications it is often expressed in
decibels (dB). The minimum possible crest factor is 1, 1:1 or 0 dB.
Crest factor can be used to detect the existence of a current
pulse. A sharp peak corresponds to a relatively higher value of
crest factor. The crest factor of a waveform is equal to the peak
amplitude of a waveform divided by the RMS value:
C=|I.sub.peak|/I.sub.rms
wherein:
[0128] I.sub.peak is the current's peak amplitude; and
[0129] I.sub.rms is the current's RMS value.
[0130] Three non-limiting example V-I trajectory load features 176
include: (f7) area; (f8) eccentricity; and (f9) Hausdorff
distance.
[0131] The Hausdorff distance, or Hausdorff metric, also called
Pompeiu-Hausdorff distance, measures how far two subsets of a
metric space are from each other. It turns the set of non-empty
compact subsets of a metric space into a metric space in its own
right. The Hausdorff distance is the longest distance one can be
forced to travel by an adversary who chooses a point in one of the
two sets, from where you then must travel to the other set. In
other words, it is the farthest point of a set that you can be to
the closest point of a different set.
[0132] While specific embodiments of the disclosed concept have
been described in detail, it will be appreciated by those skilled
in the art that various modifications and alternatives to those
details could be developed in light of the overall teachings of the
disclosure. Accordingly, the particular arrangements disclosed are
meant to be illustrative only and not limiting as to the scope of
the disclosed concept which is to be given the full breadth of the
claims appended and any and all equivalents thereof.
* * * * *